Regression modeling of restricted mean survival time under length-biased sampling data

Restricted mean survival time (RMST) is of significant clinical interest in survival analysis. When evaluating the effects of covariates, it is often preferable to directly model RMST on the covariates. However, existing RMST methods exhibit limitations, particularly when data are subject to length-biased samplings. Length-biased data is frequently encountered in observational studies, such as those in labor economics, cancer screening trials, and HIV prevalent cohort studies. In such cases, the data is not a random sample of the underlying population, making bias challenging to eliminate through study design. Ignoring this bias can lead to erroneous conclusions. To address this, we model RMST directly on covariates using a generalized linear model under the setting of length-biased sampling. We have developed two novel methods based on pseudo observations. Given that length-biased data contains auxiliary information indicating that truncation time and residual time share the same distribution, we incorporate this information into our estimations, enhancing estimation efficiency. Moreover, our approaches offer the advantages of robustness and computational simplicity. Our proposed methods are evaluated in simulation studies and applied to real data analyses.